Answer:
<em>$180.</em>
Step-by-step explanation:
First lets find the <em>interest rate.</em>
<em>6.1 ÷ 100 = 0.061</em>
<em>0.061 x $200 = 12.2</em>
based on the calculations, <em>12.2</em> is our interest rate <em>in a year</em>. Now lets find the interest rate in <em>15 years</em>.
<em>12.2 x 15 = $183 </em>
So <em>$183</em> is our<em> precise</em> interest rate in <em>15 years</em>, but lets<em> round the interest rate to the nearest 10 dollars.</em> Therefore, <em>$180 is our answer.</em>
Answer:
x = 50*e∧ -t/100
Step-by-step explanation:
We assume:
1.-That the volume of mixing is always constant 300 gallons
2.-The mixing is instantaneous
Δ(x)t = Amount in - Amount out
Amount = rate * concentration*Δt
Amount in = 3 gallons/ min * 0 = 0
Amount out = 3 gallons/min * x/ 300*Δt
Then
Δ(x)t/Δt = - 3*x/300 Δt⇒0 lim Δ(x)t/Δt = dx/dt
dx/dt = - x/100
dx/ x = - dt/100
A linear first degree differential equation
∫ dx/x = ∫ - dt/100
Ln x = - t/100 + C
initial conditions to determine C
t= 0 x = 50 pounds
Ln (50) = 0/100 * C
C = ln (50)
Then final solution is:
Ln x = - t/100 + Ln(50) or
e∧ Lnx = e ∧ ( -t/100 + Ln(50))
x = e∧ ( -t/100) * e∧Ln(50)
x = e∧ ( -t/100) * 50
x = 50*e∧ -t/100
The logarithm of a product is equal to the sum of logarithms:
Drop the exponents:
The logarithm of a number is equal to 1 if the base of the logarithm is the same as the number itself:
Answer:a+b
Step-by-step explanation:
You can use the variables a and b to solve your equation if you need
